This e-book constitutes the refereed complaints of the eleventh foreign convention at the idea and alertness of Cryptology and knowledge safeguard, ASIACRYPT 2005, held in Chennai, India in December 2005.

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Extra info for Advances in Cryptology - ASIACRYPT 2005: 11th International Conference on the Theory and Application of Cryptology and Information Security, Chennai, India, December 4-8, 2005. Proceedings

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1. A table of curves recommended as international standards [16, 36]. Note that the value of cπ for each of the standards curves is small (at most 3), except for the curves in the NIST K (Koblitz curve) family. These phenomena are to be expected and are explained in Section 6. Any curve with cπ = 1 has the property that its isogeny class consists of only one level. 1 that randomly generated elliptic curves with cπ = 1 (or, more generally, with smooth cπ ) will have discrete logarithm problems of typical diﬃculty amongst all elliptic curves in their isogeny class.

1. For a holomorphic modular form f one has ap log p + O(m1/2 ). ψ(m, f ) = p≤m Proof. The error term represents the contribution of proper prime powers. 3) which is O(m1/2 ) by the Prime Number Theorem. 2. (Iwaniec [20, p. 114]) Assume that f is a holomorphic modular cusp form of level3 N and that L(s, f ) satisﬁes GRH. Then ψ(m, f ) = O(m1/2 log(m) log(mN )). 3 Actually in [20] N equals the conductor of the L-function, which in general may be smaller than the level. The lemma is of course nevertheless valid.